In the art, magnification of distant objects is usually accomplished with telescopes, for example with a classical telescope such as that shown in FIG. 1. The objective lens forms a real, reduced image I of the object O. I' is the virtual image of I formed by the ocular. The image I' may be formed anywhere between the near and far points of the eye.
In practice, the objects examined by a telescope are at such large distances from the instrument that the image I is formed very nearly at the second focal point of the objective. Furthermore, if the image I' is at infinity, the image I is at the first focal point of the ocular. The distance between objective and ocular, or the optical length of the telescope, is therefore the sum of the focal lengths of objective and ocular, f.sub.1 +f.sub.2.
The angular magnification of a telescope is defined as the ratio of the angle subtended at the eye by the final image I', to the angle subtended at the (unaided) eye by the object. As will be shown, this ratio may be expressed in terms of the focal lengths of objective and ocular. The shaded bundle of rays in FIG. 2 corresponds to that in FIG. 1, except that the object and the final image are both at infinity. The ray passing through F.sub.1, the first focal point of the objective, and through F.sub.2 ', the second focal point of the ocular, has been emphasized. The object (not shown) subtends an angle .theta. at the objective and would subtend essentially the same angle at the unaided eye. Also, since the observer's eye is placed just to the right of the focal point F.sub.2 ', the angle subtended at the eye by the final image is very nearly equal to the angle .theta.'. The distances ab and cd are equal to one another and to the height y' of the image I. Since both .theta. and .theta. ' are small, they may be approximated by their tangents. It can be seen from the right triangles F.sub.1 ab and F.sub.2 'cd that .theta.=-y'/f.sub.1 and .theta.'=y'/f.sub.2. Hence, the magnification M is given by EQU M=.theta.'/.theta.=-(y'/f.sub.2)/(y'/f.sub.1)=-f.sub.1 /f.sub.2.
The angular magnification of a classical telescope is therefore equal to the ratio of the focal length of the objective to that of the ocular. The minus sign denotes an inverted image.
Although classical telescopes may be used with such a left for right inverted image without significant disadvantage for astronomical observations, it is desirable that a terrestrial telescope form an erect image. This may be accomplished by the insertion of an erecting lens or lens systems between the objective and ocular. The erecting lens simply serves to invert the image formed by the objective. That is the optical system of the spyglass. It has the disadvantage of requiring an unduly long tube, since four times the focal length of the erecting lens must be added to the sum of focal lengths of objective and ocular. Furthermore, classical telescopes typically have poor eye relief, e.g. about only an inch or two and the eye must be accurately centered on the telescope optical axis for viewing.
The problems of excess length and image inversion have been remedied with the introduction of the Galilean telescope, another form of the classical telescope which obeys the same magnification rule derived above. In the Galilean telescope, the ocular is a double concave lens as illustrated in FIG. 3, and the objective is a double convex lens as for the classical telescope described above. In the Galilean telescope, the objective is configured to focus an image at a point behind the ocular. Hence, there is a virtual object at a distance x.sub.2 from the ocular. The distance between the lenses, x.sub.1 +x.sub.2 =f(+)+f'(-), where f(+) is the infinity focal length of the positive lens (objective), and f'(-) is the infinity focal length (virtual) of the negative lens. The Galilean telescope is only in focus if x.sub.2 =-f'(-) for real objects at infinity. The Galilean telescope must be refocused for observing objects not at infinity. With the Galilean telescope, the virtual image is erect, and the eye relief is as long as any arbitrary distance from the eye to the eye lens (i.e. ocular) of the Galilean telescope, but the eye must still be accurately centered. Positioning the eye at the exit pupil as necessary for the classical telescope or centering the eye on the instrument optical axis or refocusing is a significant limitation to employing any telescope while operating a moving automobile or other vehicle.
Another magnifier with which most people are familiar is the "loupe". A typical loupe is illustrated in FIG. 4. The loupe consists of only one positive lens and does produce erect virtual images that do not require accurate centering or positioning of the eye. However, the viewed object cannot be located at a long distance from the lens, since the object must be viewed inside of focus.
What is needed, especially for use in a moving vehicle, is a magnifier for which objects to be viewed can be at any arbitrarily large distance from the magnifier, that does not require accurate centering of the eye at the exit pupil of the instrument, that does not require centering of the eye on the optic axis of the instrument, that does not require refocusing, and that still provides erect, non-inverted images to the viewer.